Question 3: Write two proper subsets of each of the following sets:
\((iii)\) \(\;\) \(N \)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(\{1,2,3\}\)
\( (ii) \; \) \(\{4,5,6\}\)
Explanation:
Since \(N\) is an infinite set, it has infinitely many subsets and infinitely many proper subsets.
A proper subset of a set is a subset that is not equal to the original set.
The subsets \(\{1,2,3\}\) and \(\{4,5,6\}\) both contain some (but not all) elements of the original set.